Sr Examen

Otras calculadoras

Resolución de integrales/ x²+x+1/ (2x²+4)/(x³-x²+x+1)

Integral de (2x²+4)/(x³-x²+x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   ___                  
 \/ 3                   
 -----                  
   3                    
   /                    
  |                     
  |          2          
  |       2*x  + 4      
  |   --------------- dx
  |    3    2           
  |   x  - x  + x + 1   
  |                     
 /                      
 0
∫0332x2+4(x+(x3−x2))+1 dx\int\limits_{0}^{\frac{\sqrt{3}}{3}} \frac{2 x^{2} + 4}{\left(x + \left(x^{3} - x^{2}\right)\right) + 1}\, dx 
Integral((2*x^2 + 4)/(x^3 - x^2 + x + 1), (x, 0, sqrt(3)/3))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                   
 |                                                                                                                                                                    
 |        2                          /                                    /                      2\\            /                           /               2       \\
 |     2*x  + 4                      |    3       2                       |13       110*t   176*t ||            |    3                      |  3        88*t    66*t||
 | --------------- dx = C + 2*RootSum|44*t  - 44*t  + 14*t - 1, t -> t*log|-- + x - ----- + ------|| + 4*RootSum|44*t  - 2*t - 1, t -> t*log|- -- + x - ----- + ----||
 |  3    2                           \                                    \7          7       7   //            \                           \  17         17     17 //
 | x  - x  + x + 1                                                                                                                                                    
 |                                                                                                                                                                    
/
∫2x2+4(x+(x3−x2))+1 dx=C+4RootSum⁡(44t3−2t−1,(t↦tlog⁡(−88t217+66t17+x−317)))+2RootSum⁡(44t3−44t2+14t−1,(t↦tlog⁡(176t27−110t7+x+137)))\int \frac{2 x^{2} + 4}{\left(x + \left(x^{3} - x^{2}\right)\right) + 1}\, dx = C + 4 \operatorname{RootSum} {\left(44 t^{3} - 2 t - 1, \left( t \mapsto t \log{\left(- \frac{88 t^{2}}{17} + \frac{66 t}{17} + x - \frac{3}{17} \right)} \right)\right)} + 2 \operatorname{RootSum} {\left(44 t^{3} - 44 t^{2} + 14 t - 1, \left( t \mapsto t \log{\left(\frac{176 t^{2}}{7} - \frac{110 t}{7} + x + \frac{13}{7} \right)} \right)\right)}
Simplificar
Gráfica
0.000.050.100.150.200.250.300.350.400.450.500.55-1010
Trazar el gráfico f(x)
Respuesta [src] 
                                                            /                               /       ___    \\
         / 3      2                              \          | 3      2                      |     \/ 3     ||
- RootSum\t  - 2*t  + 2*t - 2, t -> t*log(-1 + t)/ + RootSum|t  - 2*t  + 2*t - 2, t -> t*log|-1 + ----- + t||
                                                            \                               \       3      //
−RootSum⁡(t3−2t2+2t−2,(t↦tlog⁡(t−1)))+RootSum⁡(t3−2t2+2t−2,(t↦tlog⁡(t−1+33)))- \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 + \frac{\sqrt{3}}{3} \right)} \right)\right)} 
=
= 
                                                            /                               /       ___    \\
         / 3      2                              \          | 3      2                      |     \/ 3     ||
- RootSum\t  - 2*t  + 2*t - 2, t -> t*log(-1 + t)/ + RootSum|t  - 2*t  + 2*t - 2, t -> t*log|-1 + ----- + t||
                                                            \                               \       3      //
−RootSum⁡(t3−2t2+2t−2,(t↦tlog⁡(t−1)))+RootSum⁡(t3−2t2+2t−2,(t↦tlog⁡(t−1+33)))- \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 + \frac{\sqrt{3}}{3} \right)} \right)\right)} 
-RootSum(_t^3 - 2*_t^2 + 2*_t - 2, Lambda(_t, _t*log(-1 + _t))) + RootSum(_t^3 - 2*_t^2 + 2*_t - 2, Lambda(_t, _t*log(-1 + sqrt(3)/3 + _t)))
Respuesta numérica [src] 
1.99978262443133
1.99978262443133

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор